Conventionally, various image processing technologies of removing noise in an input image have been developed. For example, a simple smoothing filter is simple in method, and can be designed at low cost, so that it has been employed by a number of image devices. Moreover, according to the simple smoothing filter, an edge signal of an object is smoothed together, therefore, a filter that smoothes anything other than the edge (an edge-preserved smoothing filter) has been recently developed.
According to the edge-preserved smoothing filter, filtering processing is executed by weighting peripheral pixels to be applied to the smoothing filter in accordance with a difference in pixel level from a pixel to be smoothed. In other words, according to the edge-preserved smoothing filter, the filtering processing is performed on peripheral pixels with small level differences from pixels to be smoothed by assigning a relatively large weight, and on peripheral pixels with large level differences by assigning a relatively small weight, or setting the weight to zero.
However, according to a conventional smoothing filter, when there are fine gradation information and an edge (for example, a boundary between a bright part and a dark part) in the same band that includes a noise component to be removed, they are to be removed together with the noise. Moreover, according to the edge-preserved smoothing filter having the edge-preserving function described above, its effect can be obtained when the fine gradation information and the edge have an amplitude equal to or larger than the amplitude of a noise component; however, information having an amplitude smaller than the amplitude of the noise component is to be removed. In terms of quality, discontinuous gradation is sometimes produced in a smooth area in some cases.
As a technology of removing such noise, a noise removal technology that uses a frequency filter, such as a wavelet transform, has been known. For example, by using the wavelet transform, an input image (original image) is separated into a plurality of frequency bands, and threshold processing (coring) is performed in each of the frequency bands. According to the wavelet transform, an optimal threshold can be adjusted by band of frequency, so that noise removal can be performed while keeping a high image quality, compared with a real space filter, such as a smoothing filter.
Patent Document 1: Japanese Laid-open Patent Publication No. 2000-105815
Patent Document 2: Japanese Laid-open Patent Publication No. 2006-310999
Patent Document 3: Japanese Laid-open Patent Publication No. 2005-234001
However, according to the above conventional technologies, there is a problem that ringing occurs and degrades the image quality, or the image quality of a noise-removed image is poor, consequently, noise removal with high precision may not be achieved.
For example, according to a noise removal technology by multiresolution transform processing using such as the wavelet transform, resulting from noise removal, an artifact called ringing is produced around a steep edge having a large change in pixel level value. A cause of occurrence of ringing is explained below by using an example that an image is represented by a one-dimensional signal, as depicted in FIG. 9A. Each of FIGS. 9A to 9D is a schematic diagram that schematically depicts a graph in which the axis of ordinate represents pixel value (for example, the value of brightness), and the axis of abscissa represents the position of pixel.
According to the multiresolution transform processing described above, as depicted in FIG. 9B, an input image (an original signal in FIG. 9A) is separated into two signals, namely, a low frequency component and a high frequency component, by performing the wavelet transform on the input image. For the purpose of simplifying explanation, described here is the example of separating into two signals of a low frequency component and a high frequency component; however, it can be separated into signals in a plurality of frequency bands. After noise removal is performed only on the separated high frequency component as depicted in FIG. 9C, an inverse wavelet transform using the separated low frequency component and the noise-removed high frequency component is performed as depicted in FIG. 9D, and then a noise-removed image is obtained.
In this way, according to the noise removal through the multiresolution transform processing, a small amplitude of a high frequency component obtained by separation is to be turned smaller or to be turned to zero, therefore, a reconstructed signal basically represents directly a signal form of a low frequency component of which amplitude is not reduced. A signal of a rectangular wave of, such as an edge in image, can be expressed only as a composite wave of a plurality of frequency-band signals in a complicated shape. When an input signal is a signal having a steep edge with a large change in pixel level value, the input signal is separated into a high frequency component and a low frequency component as depicted in FIG. 9B, so that a change in the low frequency component around the edge that is not observed in the original signal appears as “a change as like waves in the brightness value (ringing)” in a reconstructed signal. In other words, performing noise removal processing using the multiresolution transform processing on an image having a steep edge with a large change in pixel level value leads to occurrence of ringing.
Moreover, a noise removal technology using a real space filter, such as the smoothing filter or the edge-preserved smoothing filter described above, can prevent occurrence of ringing described above. However, according to the noise removal technology using a real space filter, coring processing (optimal signal control band by band of frequency) may not be performed as performed by the noise removal technology using a frequency filter, such as the wavelet transform. Therefore, the image quality of an image obtained by the noise removal technology using a real space filter is not as good as the image quality by the noise removal technology using a frequency filter.